| Peer-Reviewed

Numerical Solutions of 2-D Incompressible Driven Cavity Flow with Wavy Bottom Surface

Received: 15 November 2014     Accepted: 26 November 2014     Published: 27 December 2014
Views:       Downloads:
Abstract

In the present numerical study is devoted to investigate the lid-driven cavity flow with wavy bottom surface. The cavity upper wall is moving with a uniform velocity by unity and the other walls are no-slip. The physical problem is represented mathematically by a set of governing equations and the developed mathematical model is solved by employing Galerkin weighted residual method of finite element formulation. The wide ranges of governing parameters, i. e., the Reynolds number (Re), and the number of undulations (λ) on the flow structures are investigated in detail. The behavior of the force coefficient Cf also has been examined. Streamline plots provide the details of fluid flow. The fluid contained inside a squared cavity is set into motion by the top wall which is sliding at constant velocity from left to right and the undulation which was induced at the bottom surface. It is found that these parameters have significant effect on the flow fields in the cavity. Furthermore, the trends of skin friction for different values of the aforementioned parameters are presented in this investigation.

Published in American Journal of Applied Mathematics (Volume 3, Issue 1-1)

This article belongs to the Special Issue Fluid Flow and Heat Transfer Inside a Closed Domain

DOI 10.11648/j.ajam.s.2015030101.14
Page(s) 30-42
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2014. Published by Science Publishing Group

Keywords

Skin Friction; Lid Driven Cavity; Numerical Study, Wavy Surface

References
[1] Shankar PN, Deshpande MD., Fluid mechanics in the driven cavity, Ann Rev Fluid Mech 2000; 32:93–136.
[2] Robert NM, Pavageau M, Rafailidis S, Schatzmann M. Study of line source characteristics for 2-D physical modeling ofpollutant dispersion in street canyons, Journal of Wind Engineering and Industrial Aerodynamics, 1996; 62: 37—56.
[3] R. Iwatsu, J.M. Hyun, Three-dimensional driven-cavity flows with a vertical temperature gradient, Int. J. Heat Mass Transfer 38 (1995)3319–3328.
[4] A.A. Mohamad, R. Viskanta, Transient low Prandtl number fluid convection in a lid-driven cavity, Num. Heat Transfer: Part A 19(1991) 187–205.
[5] A.K. Prasad, J.R. Koseff, Combined forced and natural convection heat transfer in a deep lid-driven cavity flow, Int. J. Heat Fluid Flow 17 (1996) 460–467.
[6] C.F. Freitas, R.L. Street, Non-linear transient phenomena in a complex recirculating flow: A numerical investigation, Int. J. Num. Methods Fluids 8 (1988) 769–802
[7] A.A. Mohamad, R. Viskanta, Flow and heat transfer in a lid-driven cavity with stably stratified fluid, Appl. Math. Model 19 (1995) 465–472.
[8] K.M. Khanafer, A.J. Chamkha, Mixed convection flow in a lid driven enclosure with a fluid-saturated porous medium, Int. J. Heat Mass Transfer 42 (1999) 2465–2481.
[9] C.-J. Chen, H. Nassari-Neshat, K.-S. Ho, Finite-analytical numerical solution of heat transfer in two-dimensional cavity flow, Num. Heat Transfer 4 (1981) 179–197.
[10] R. Iwatsu, J.M. Hyun, K. Kuwahara, Convection in a differentially heated square cavity with a torsionally-oscillating lid, Int. J. Heat Mass Transfer 35 (1992) 1069–1076.
[11] R. Iwatsu, J.M. Hyun, K. Kuwahara, Numerical simulation of flows driven by a torsionally oscillating lid in a square cavity, J. Fluids Eng. 114 (1992) 143–149.
[12] Abdalla Al-Amiri, K. Khanafer, I. Pop, Numerical simulation of unsteady mixed convection in a driven cavity using an externally excited sliding lid, Eur. J. Mech. B/Fluids, in press
[13] V.S. Arpaci, P.S. Larsen, Convection Heat Transfer, Prentice-Hall, 1984, p. 90.
[14] O. Aydın, Aiding and opposing mechanisms of mixed convection in a shear-and buoyancy-driven cavity, Int. Comm. Heat Mass Transfer 26 (1999) 1019–1028.
[15] A.J. Chamkha, Hydromagnetic combined convection flow in a vertical lid-driven cavity with internal heat generation or absorption, Num. Heat Transfer: Part A 41 (2002) 529–546.
[16] E. Erturk, T. C. Corke2 and C. C. Gokcol, Numerical solutions of 2-D steady incompressible driven cavity flow at high Reynolds numbers, International Journal For Numerical Methods In Fluids, 2005; 48:747–774
[17] E. Erturk and O. Gokcol, Fine grid numerical solutions of triangular cavity flow, The European Physical Journal Applied Physics, 2007, 38, 97–105
[18] C. Migeon, A. Texier, G. Pineau, Effects of lid driven cavity shape on the flow establishment phase, J. Fluids Struct. 14 (2000) 469–488.
[19] R. Glowinski, G. Guidoboni, T.W. Pan, Wall driven incompressible viscous flow in a two-dimensional semi-circular cavity, J. Comput. Phys. 216 (2006) 76–91.
[20] H. Mercan, K. Atalık,Vortex formation in lid-driven arc-shape cavity flows at high Reynolds numbers, European Journal of Mechanics B/Fluids 28 (2009) 61–71
[21] S. Ostrach, Natural convection in enclosures, in: J.P. Hartnett, T.F. Irvine Jr. (Eds.), Advances in Heat Transfer, vol. 8, Academic Press, New York, 1972, pp. 161–227.
[22] I. Catton, Natural convection in enclosures, in: Proceedings of the Sixth International Heat Transfer Conference, vol. 6, 1978, pp. 13–31.
[23] K.T. Yang, Transitions and bifurcations in laminar buoyant flows in confined enclosures, J. Heat Transfer 110 (1988) 1191–1204.
[24] Sheikholeslami, M., Gorji-Bandpy, M., Pop, I. & Soleimani, S. (2013). Numerical study of natural convection between a circular enclosure and a sinusoidal cylinder using control volume based finite element method. International Journal of Thermal Sciences, Vol. 72, pp. 147-158.
[25] C. Taylor, P. Hood, A numerical solution of the Navier–Stokes equations using finite element technique, Computers & Fluids 1 (1) (1973) 73–89
[26] P. Dechaumphai, Finite Element Method in Engineering, 2nd ed. Chulalongkorn University Press, Bangkok, 1999.
[27] N. P. Moshkin, K. Poochinapan, Novel finite difference scheme for the numerical solution of two-dimensional incompressible Navier-Stokes equations, International Journal Of Numerical Analysis And Modeling, 7(2)(2010) 321–329
[28] K. Poochinapan and Chiang Mai, Numerical Implementations for 2-D Lid Driven Cavity Flow in Stream Function Formulation”, ISRN Applied Mathematics, 2012 (2012), pp. - 1-17.
Cite This Article
  • APA Style

    K. M. Salah Uddin, Litan Kumar Saha. (2014). Numerical Solutions of 2-D Incompressible Driven Cavity Flow with Wavy Bottom Surface. American Journal of Applied Mathematics, 3(1-1), 30-42. https://doi.org/10.11648/j.ajam.s.2015030101.14

    Copy | Download

    ACS Style

    K. M. Salah Uddin; Litan Kumar Saha. Numerical Solutions of 2-D Incompressible Driven Cavity Flow with Wavy Bottom Surface. Am. J. Appl. Math. 2014, 3(1-1), 30-42. doi: 10.11648/j.ajam.s.2015030101.14

    Copy | Download

    AMA Style

    K. M. Salah Uddin, Litan Kumar Saha. Numerical Solutions of 2-D Incompressible Driven Cavity Flow with Wavy Bottom Surface. Am J Appl Math. 2014;3(1-1):30-42. doi: 10.11648/j.ajam.s.2015030101.14

    Copy | Download

  • @article{10.11648/j.ajam.s.2015030101.14,
      author = {K. M. Salah Uddin and Litan Kumar Saha},
      title = {Numerical Solutions of 2-D Incompressible Driven Cavity Flow with Wavy Bottom Surface},
      journal = {American Journal of Applied Mathematics},
      volume = {3},
      number = {1-1},
      pages = {30-42},
      doi = {10.11648/j.ajam.s.2015030101.14},
      url = {https://doi.org/10.11648/j.ajam.s.2015030101.14},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajam.s.2015030101.14},
      abstract = {In the present numerical study is devoted to investigate the lid-driven cavity flow with wavy bottom surface. The cavity upper wall is moving with a uniform velocity by unity and the other walls are no-slip. The physical problem is represented mathematically by a set of governing equations and the developed mathematical model is solved by employing Galerkin weighted residual method of finite element formulation. The wide ranges of governing parameters, i. e., the Reynolds number (Re), and the number of undulations (λ) on the flow structures are investigated in detail. The behavior of the force coefficient Cf also has been examined. Streamline plots provide the details of fluid flow. The fluid contained inside a squared cavity is set into motion by the top wall which is sliding at constant velocity from left to right and the undulation which was induced at the bottom surface. It is found that these parameters have significant effect on the flow fields in the cavity. Furthermore, the trends of skin friction for different values of the aforementioned parameters are presented in this investigation.},
     year = {2014}
    }
    

    Copy | Download

  • TY  - JOUR
    T1  - Numerical Solutions of 2-D Incompressible Driven Cavity Flow with Wavy Bottom Surface
    AU  - K. M. Salah Uddin
    AU  - Litan Kumar Saha
    Y1  - 2014/12/27
    PY  - 2014
    N1  - https://doi.org/10.11648/j.ajam.s.2015030101.14
    DO  - 10.11648/j.ajam.s.2015030101.14
    T2  - American Journal of Applied Mathematics
    JF  - American Journal of Applied Mathematics
    JO  - American Journal of Applied Mathematics
    SP  - 30
    EP  - 42
    PB  - Science Publishing Group
    SN  - 2330-006X
    UR  - https://doi.org/10.11648/j.ajam.s.2015030101.14
    AB  - In the present numerical study is devoted to investigate the lid-driven cavity flow with wavy bottom surface. The cavity upper wall is moving with a uniform velocity by unity and the other walls are no-slip. The physical problem is represented mathematically by a set of governing equations and the developed mathematical model is solved by employing Galerkin weighted residual method of finite element formulation. The wide ranges of governing parameters, i. e., the Reynolds number (Re), and the number of undulations (λ) on the flow structures are investigated in detail. The behavior of the force coefficient Cf also has been examined. Streamline plots provide the details of fluid flow. The fluid contained inside a squared cavity is set into motion by the top wall which is sliding at constant velocity from left to right and the undulation which was induced at the bottom surface. It is found that these parameters have significant effect on the flow fields in the cavity. Furthermore, the trends of skin friction for different values of the aforementioned parameters are presented in this investigation.
    VL  - 3
    IS  - 1-1
    ER  - 

    Copy | Download

Author Information
  • Department of Management Information Systems, University of Dhaka, Dhaka, Bangladesh

  • Deparment of Applied Mathematics, University of Dhaka, Dhaka, Bangladesh

  • Sections